Motivated by Goldbacher, Euler proved many formulas for double zeta values. The most well-known ones are his Sum Formula and Decomposition Formula. After multiple zeta values were introduced in the 1990s, Euler’s Sum Formula was quickly generalized in quite a few directions. However, Euler’s Decomposition Formula was generalized to multiple zeta values only recently by the method of double shuffle relations. We will explain how to make sense of Euler’s formula in the multiple variable case and discuss some of the generalizations.
Li Guo